Phd records
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A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenWed, 31 Jan 2024 19:16:15 +0000Homogeneous sequences of cardinals for ordinal definable partition relations
https://resolver.caltech.edu/CaltechETD:etd-06132007-073731
Authors: {'items': [{'id': 'Kafkoulis-G', 'name': {'family': 'Kafkoulis', 'given': 'George'}, 'show_email': 'NO'}]}
Year: 1990
DOI: 10.7907/hchw-ca34
NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document.
In this dissertation we study the consistency strength of the theory ZFC & ([...] strong limit)([...] < [...])([...]) (*), and we prove the consistency of this theory relative to the consistency of the existence of a supercompact cardinal and an inaccessible above it. If U is a normal measure on [...], then [...] denotes the Supercompact Prikry forcing induced by U. [...] is the partition relation [...] except that we consider only OD colorings of [...]. Theorems 1,2 are the main results of our thesis.
Theorem 1. If there exists a model of ZFC in which [...] is a supercompact cardinal and [...] is an innaccessible above [...], then we can construct a model V of the same properties with the additional property that if U is a normal [...]-measure and G is [...] - generic over V, then V[G] does not satisfy the [...] partition property. [...]
If G is a [...]-generic over V filter, then we define H to be the set H: [...], and we consider the inner model V(H), which is the smallest inner model of ZF that contains H as an element. We prove that V(H) satisfies the above partition property (*).
Moreover, V(H) satisfies < [...] - DC and using this fact we define a forcing [...], which is almost-homogeneous, < [...] - closed forcing that forces the AC over V(H) and does not add any new sets of rank < [...].
Theorem 2. If [...] is [...] -generic over V(H) and V[...], then [...] + [...] strong limit + [...]. Therefore Con(ZFC + ([...]) [...] supercompact & [...] inaccessible & is [...]) [...] Con(ZFC + ([...] strong limit)[...]. [...]
https://thesis.library.caltech.edu/id/eprint/2572